An important consideration in the design and development of numeracy-focused coursework is ensuring that one meets students where they are with respect to both their mathematics background and their existing numeracy practices in relation to public issues. The latter consideration is especially important, given that students already think about…

Interest in the role of casuistry and casuistical questions in Kant's "Doctrine of Virtue" ("DV"), i.e. the second part of the "Metaphysics of Morals," has grown in recent years. My own position is formulated in Schuessler (2012, in German), the main thesis of which will be retained here in an updated form and with…

This concise, digestible book shows how the cultivation of reason became the defining aim of western education, and critiques how this aim has been eclipsed in recent decades by the neoliberal system of mass schooling imposed by the state. Chapters outline succinctly the history of western education and its origins in Ancient Greece, demonstrating…

The purpose of this proposed quantitative, ex post facto, comparative study with a pretest-posttest design was to assess gains in overall Critical Thinking (CT) skills, and particularly in the Hypothetical-deductive Reasoning (HDR) skills, for pre-health college students tested before and after a Critical Analyses in Science course they attended…

This article reports on a qualitative investigation into students' thinking about a differential equations problem posing task; i.e. an initial value problem. Analysis of written and verbal responses to the task indicate that only four of the 34 students who participated in the study were successful in posing problems. Furthermore, only one of the…

This study identifies characteristics of polygon class learning opportunities for 8-9-year-old children during the whole-class instruction. We consider the interplay between the geometrical tasks demanding different ways of reasoning, features of children's geometrical thinking, and the teacher's moves to identify characteristics of learning…

Human decision-making is underpinned by distinct systems that differ in flexibility and associated cognitive cost. A widely accepted dichotomy distinguishes between a cheap but rigid model-free system and a flexible but costly model-based system. Typically, humans use a hybrid of both types of decision-making depending on environmental demands.…

University students are often asked to learn abstract concepts. Abstract concepts are hard to learn. Giving specific examples can help learning abstract concepts. These examples might limit understanding to the similarities between the abstract domain and particular examples. The primary purpose of this study was to test whether exposure to…

Capacities for abstract thinking and problem-solving are central to human cognition. Processes of abstraction allow the transfer of experiences and knowledge between contexts helping us make informed decisions in new or changing contexts. While we are often inclined to relate such reasoning capacities to individual minds and brains, they may in…

This paper reports the statistical and probabilistic reasoning of young children in terms of randomness, variability, and data representations in the context of informal inferential reasoning (IIR). Using the IIR approach, a task was designed and conducted one-on-one with 28 children aged 5 to 6 years old, in a case study setting. The researcher…

The construct of static and emergent shape thinking (Moore & Thompson, 2015) characterizes differences in students' reasoning about graphs. In our previous work with middle school students, we found that this construct may also be useful in characterizing students' reasoning about other representations such as simulations and tables. In this…

There is growing interest in the construct of "transduction", first introduced by (Kress, Cope and Kalantzis (eds), Multiliteracies: Literacy learning and the design of social futures pp.153-161, Routledge, 2000), p. 159) to name how meanings in one mode are remade in another. Science educators now broadly agree that students need to…

Moral decisions often involve dilemmas: cases of conflict between competing obligations. In two studies (N = 204), we ask whether children appreciate that reasoning through dilemmas involves acknowledging that there is no single, simple solution. In Study 1, 5- to 8-year-old US children were randomly assigned to a Moral Dilemma condition, in which…

Siegel claimed that teachers are obliged to provide grounds whenever demanded, as a result of which they must be able to subject to scrutiny whatever they teach. In this paper, however, and taking as a reference Wittgenstein's "On Certainty," it is shown that such a demand cannot work for second language teachers because their main task…

Education researchers are deeply interested in understanding the way students organize their knowledge. Card sort tasks, which require students to group concepts, are one mechanism to infer a student's organizational strategy. However, the limited resolution of card sort tasks means they necessarily miss some of the nuance in a student's strategy.…